The standard modularity, equation REF , is equal to the trace of this matrix divided by \(2E\) . Following [1]}, it is convenient to change the sum over nodes in equation REF  to a sum over blocks. Defining
\(\Sigma _{ab} &= \sum _{i \in a, j \in b} A_{ij} \\T_{a} &= \sum _{i \in a} k_i\) 
